Generally, when your neighbor's tree falls onto your property and causes damage, it is considered an Act of God, and you neighbor is not responsible for the damage. The exception to that is if your neighbor has failed perform necessary maintenance on the tree. You should talk to your neighbor about the potential damage that can be caused by the trees and suggest that he take them down. If you are unsure of your rights and responsibilities as a property owner, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
If the trees were alive and well-maintained, then you would be responsible for any branches that fell into your yard. However, if the trees are all dead and one has already created damage to your yard, the trees are now a nuisance and can be treated as such. You should write a letter to your local municipality with pictures of the dead trees (and, if you have them, pictures of the tree that fell) and copy your neighbor on the letter. The city/county can order that the trees be removed. If you get no response, you may need to have an administrative law attorney handle this matter for you.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : firstname.lastname@example.org : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.